x(x+14)=66

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Solution for x(x+14)=66 equation: 


Simplifying
x(x + 14) = 66

Reorder the terms:
x(14 + x) = 66
(14 * x + x * x) = 66
(14x + x2) = 66

Solving
14x + x2 = 66

Solving for variable 'x'.

Reorder the terms:
-66 + 14x + x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 14x + 66 + x2 = 0 + 66

Reorder the terms:
-66 + 66 + 14x + x2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 14x + x2 = 0 + 66
14x + x2 = 0 + 66

Combine like terms: 0 + 66 = 66
14x + x2 = 66

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 66 + 49

Reorder the terms:
49 + 14x + x2 = 66 + 49

Combine like terms: 66 + 49 = 115
49 + 14x + x2 = 115

Factor a perfect square on the left side:
(x + 7)(x + 7) = 115

Calculate the square root of the right side: 10.723805295

Break this problem into two subproblems by setting 
(x + 7) equal to 10.723805295 and -10.723805295.


Subproblem 1
x + 7 = 10.723805295

Simplifying
x + 7 = 10.723805295

Reorder the terms:
7 + x = 10.723805295

Solving
7 + x = 10.723805295

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = 10.723805295 + -7

Combine like terms: 7 + -7 = 0
0 + x = 10.723805295 + -7
x = 10.723805295 + -7

Combine like terms: 10.723805295 + -7 = 3.723805295
x = 3.723805295

Simplifying
x = 3.723805295


Subproblem 2
x + 7 = -10.723805295

Simplifying
x + 7 = -10.723805295

Reorder the terms:
7 + x = -10.723805295

Solving
7 + x = -10.723805295

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = -10.723805295 + -7

Combine like terms: 7 + -7 = 0
0 + x = -10.723805295 + -7
x = -10.723805295 + -7

Combine like terms: -10.723805295 + -7 = -17.723805295
x = -17.723805295

Simplifying
x = -17.723805295


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.723805295, -17.723805295}

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